Answer:
3y² + 7y + 4 = (3x + 4)(x + 1)
Step-by-step explanation:
* To factor a trinomial in the form ax² ± bx ± c:
- Look at the c term
# If the c term is positive
∵ c = r × s ⇒ r and s are the factors of c
∴ r and s will have the same sign (sign of b)
∵ a = h × k ⇒ h , k are the factors of a
∴ rk + hs = b
∴ (hx + r)(kx + s) ⇒ if b +ve OR (hx - r)(kx - s) ⇒ if b -ve
# If the c term is negative
∵ c = r × s ⇒ r and s are the factors of c
∴ r and s will not have the same sign
∵ a = h × k ⇒ h and k are the factors of a
∴ rk - hs = b OR hs - rk = b
(hx + r)(kx - s) OR (hx - r)(kx + s)
* Now lets solve the problem
∵ 3y² + 7y + 4
∵ ax² + bx + c
∴ a = 3 , b = 7 , c = 4
∵ a = h × k
∵ 3 = 3 × 1
∴ h = 3 , k = 1
∵ c = r × s
∵ 4 = 4 × 1
∴ r = 4 , s = 1
∵ c is positive
∴ hs + rk = b
∴ 3(1) + 4(1) = 7 ⇒ same value of b
∴ 3y² + 7y + 4 = (3x + 4)(x + 1)
Answer:- A. Rectangle ABCD was translated 8 units left and then 7 units down.
Explanation:-
We can see vertex A(2,4) of rectangle ABCD moves to A"(-6,-3), in a way that A translated 8 units left (-8)and 7 units down(-7) to A".
i.e.(2-8,4-7)=(-6,-3)
Similarly the other vertices of rectangle ABCD moves to form rectangle A"B"C"D"
B (2,2) → B" (-6,-5)
C (6,2) → C" (-2,-5)
D(6,4) → D" (-2,-3)
84,75,90,87,99,91,85,88,76,92,94
Maslowich
Thank you for the free points
Answer:
Step-by-step explanation:
The Pythagorean theorem applies to right angled triangles only.
However, for any other triangle, by dropping a perpendicular from any vertex on to the opposite side, you form two right angled triangles both of which can be solved by the Pythagorean theorem.
So, the Pythagorean theorem applies to right angled triangles directly and to other triangles indirectly.
It looks like you want to compute the double integral

over the region <em>D</em> with the unit circle <em>x</em> ² + <em>y</em> ² = 1 as its boundary.
Convert to polar coordinates, in which <em>D</em> is given by the set
<em>D</em> = {(<em>r</em>, <em>θ</em>) : 0 ≤ <em>r</em> ≤ 1 and 0 ≤ <em>θ</em> ≤ 2<em>π</em>}
and
<em>x</em> = <em>r</em> cos(<em>θ</em>)
<em>y</em> = <em>r</em> sin(<em>θ</em>)
d<em>x</em> d<em>y</em> = <em>r</em> d<em>r</em> d<em>θ</em>
Then the integral is
